Path-conservative finite volume scheme with Hooke’s law-preserving paths for non-conservative hyperbolic system of hypo-elastic plastic solid

Abstract

In this paper, we propose a path-conservative finite volume scheme to address the non-conservative nature of governing equations for hypo-elastic plastic solids. By combining the Hooke’s law-preserving path with the Riemann solver, a novel class of piecewise paths is proposed. Furthermore, we process the model changes during elastic-plastic transitions by incorporating deviatoric stress iteration, establishing transition formulas, and formulating the elastic-plastic interface fluxes. Our method has been applied to both one-dimensional and two-dimensional elastic-plastic solid models. Numerical tests have demonstrated its effectiveness.